Suppression of the current instability by decay processes

A study is made of the instability of lower hybrid waves in an isothermal magnetized current-carrying plasma. It is assumed that the dynamic suppression of the current instability is associated with the excitation of a quasi-monochromatic wave near the instability threshold and its subsequent decay into two strongly damped lower hybrid waves. It is shown that the decay process results in the onset of either a quasi-periodic or stochastic nonlinear stabilization regime involving a small number of modes. The anomalous resistance is estimated.     

Nonlinear Stabilization of Resistive Instability of a Tubular Charged Particle Beam Moving above a Solid-State Plasma Cylinder

Plasma Physics Reports - Nonlinear stabilization of instability of an infinitely thin tubular electron beam moving along the surface of a solid-state plasma cylinder is analyzed. It is assumed that...     

Nonlinear theory of the collective Cherenkov interaction of a dense relativistic electron beam with a dense plasma in a waveguide

A nonlinear theory of the instability of a straight relativistic dense electron beam in a plasma waveguide is derived for conditions of the stimulated collective Cherenkov effect. A study is made of a waveguide with a dense plasma such that the plasma wave excited by the beam during the instability can be escribed, with a good degree of accuracy, as a potential wave. General relativistic nonlinear equations are btained that describe the temporal dynamics of beam-plasma instabilities with allowance for plasma nonlinearity and the generation of harmonics of the initial perturbation. Under the assumption that the resonant interaction between the beam waves and the plasma waves is weak, the general equations are reduced to relativistic equations with cubic nonlinearities by using the method of expansion in small perturbations of the trajectories and momenta of the beam and plasma electrons. The reduced equations are solved analytically, the time scales on which the instability saturates are determined, and the nonlinear saturation amplitudes are obtained. A comparison between analytical solutions to the reduced equations and numerical solutions to the general nonlinear equations shows them to be in good agreement. Nonlinear processes caused by the relativistic nature of the beam are found to prevent stochastization of the system in the nonlinear stage of the well-developed instability. In contrast, a nonrelativistic electron beam is found to be subject to significant anomalous nonlinear stochastization.     

Quantum theory of Cherenkov beam instabilities in plasma

A quantum theory of stimulated Cherenkov emission of longitudinal waves by an electron beam in an isotropic plasma is presented. The emitted radiation is interpreted as instability due to the decay of the de Broglie wave of a beam electron. Nonrelativistic and relativistic nonlinear quantum equations for Cherenkov beam instabilities are obtained. A linear approximation is used to derive quantum dispersion relations and to determine the instability growth rates. The mechanisms for nonlinear saturation of quantum Cherenkov beam instabilities are investigated, and the corresponding analytic solutions are found.     

On the Possibility of Generating Harmonics of the Electron Plasma Frequency in the Solar Atmosphere due to Explosive Instability in a System of Interpenetrating Electron and Ion Flows

An alternative mechanism is proposed for the generation of harmonics of the electron plasma frequency due to the development of explosive instability in a system of interpenetrating electron and proton flows in the solar atmosphere. The efficiency of the new mechanism in comparison with the earlier discussed mechanisms involving multistage processes of nonlinear interaction of waves in plasma is determined. It is shown that the development of explosive instability can lead to the excitation of the second and third harmonics of the plasma frequency with comparable amplitudes.     

Nonlinear theory of coupled waves exemplified by beam-plasma instability

The nonlinear stage of instability of an annular electron beam spatially separated from an annular plasma is investigated. The equations describing coupled waves for an arbitrary ratio between the beam and plasma densities are derived. It is shown that instability saturates at distances on the order of several inverse spatial growth rates. The saturation is caused by relativistic nonlinearity, generation of the second harmonic, and low-frequency modulation of the electromagnetic field. At larger distances, resonant generation of low-frequency beam oscillations becomes a dominant factor. In the case of a low-density beam, an expression for the maximum power of the generated plasma wave is obtained in an explicit form.     

Numerical simulation of the instability of a nonuniform plasma flow: Nonlinear dynamics of slipping instability

A kinetic model is proposed that describes the nonlinear dynamics of the instabilities of a transversely nonuniform plasma flow. It is shown that, in the linear approximation, the model yields the familiar boundary-value problem for the scalar potential in plasma. The slipping instability in a plane waveguide is considered as an example. The general dispersion relation for a flow with a stepwise uniform density profile and with a tangential discontinuity in its longitudinal velocity is analyzed qualitatively. The dynamics of the slipping instability is investigated numerically for a flow that is detached from the waveguide walls and whose longitudinal velocity obeys a linear, a sinusoidal, or a discontinuous distribution. In the nonlinear stage of the instability, the flow expands in such a way as to come into contact with the walls, the spread in the longitudinal velocities remains smaller than the initial velocity variation, and the longitudinal velocities of different transverse layers in the flow are not completely equalized.     

Vortex electron dynamics in a high-current plasma lens

An analytic study is made of the following problems: the instability of a plasma against the excitation of vortex turbulence, the turbulence saturation amplitude, the types and spatial structures of the nascent vortices, and their nonlinear growth rates in an electrostatic plasma lens for focusing high-current ion beams.     

Cherenkov Excitation of Spatial Waves by a Straight Nonrelativistic Electron Beam in a Plasma Waveguide

The problem of the excitation of plasma waves by a thin-walled annular electron beam in a waveguide filled entirely with a plasma is analyzed in the quasistatic approximation. The instability growth rates are derived and are studied as functions of the waveguide parameters. The evolution of different seed perturbations in the nonlinear stage of the instability is investigated.     

Classical and quantum description of electron trapping during the Cherenkov beam instability in plasma

A nonlinear quantum theory of the Cherenkov instability of a nonrelativistic monoenergetic electron beam in a cold plasma is constructed. It is shown that the instability of a low-density beam is almost purely quantum in nature and results from the emission of one quantum of a plasma wave—a plasmon—by the beam electrons. The number of emitted (and absorbed) plasmons increases with beam density, so, in the limit of high-density beams, the instability becomes a classical Cherenkov beam instability in plasma. Some analytic solutions and estimates are found, detailed numerical results are obtained, and the evolution of the quantum distribution function of the beam electrons in different regimes of the beam instability is investigated.     

Effect of the dipole-dipole interaction of particles in an active medium on the character of superradiation

The motion of a system of interacting nonlinear charged oscillators is investigated numerically. Because of nonlinearity, the total collective electric field gives rise to a phasing effect—correlations in the phases of the oscillators. The consequence is superradiation—the enhanced spontaneous short-term emission of the energy stored in the oscillators. It is shown that the oscillations of the oscillators become stochastic because of the dipole-dipole interaction between them and their nearest neighbors. As a result, as the density of the oscillators increases, distant collective correlations are suppressed, superradiation ceases to be generated, and radiation is shielded in the medium. The phenomena considered in the present paper can play an important role in cyclotron emission from a plasma and thus should be taken into account in emission calculations. The process whereby the energy of the transverse electron motion in electron cooling devices decreases is analyzed as an example. This process occurs as a result of the development of cyclotron maser instability and has the nature of superradiation. The onset of correlations between individual electrons moving in their Larmor circles is the initial, linear stage of instability developing in the plasma. Superradiation is the final, nonlinear instability stage.     

Plasma convection near the threshold for MHD instability in nonparaxial magnetic confinement systems

Using a highly nonparaxial magnetic confinement system with an internal levitated ring as an example, it is shown that, in a plasma near the threshold for ideal MHD instability, the external heating and the original local dissipative processes may give rise to and maintain self-consistent nonlinear MHD convection, which leads to an essentially nonlocal, enhanced heat transport. A closed set of equations is derived that makes it possible to describe such convective processes in a weakly dissipative plasma with β～1. Numerical simulations carried out with a specially devised computer code demonstrate that the quasisteady regime of nonlinear convection actually exists and that the marginally stable profile of the plasma pressure is maintained. A large amount of data on the structure of the nascent convective flows is obtained and analyzed.     

Stabilization of beam instability by a local instability developing due to a wave-wave interaction

A new mechanism for stabilization and suppression of beam instabilities is proposed. This mechanism, which is based on the stochastic instability of a wave-wave interaction process, plays a particularly important role in plasma systems with a small region of interaction between the beam particles and the excited waves.     

On the nonlinear theory of collective Cherenkov interaction of a high-density relativistic beam with a plasma

The nonlinear dynamics of the instability of a straight high-density relativistic electron beam under the conditions of the stimulated Cherenkov effect in a plasma waveguide is studied both analytically and numerically. It is shown that, for a beam of sufficiently high density such that the stabilizing factors are nonlinear frequency shifts and for a plasma described in a linear approximation, the basic equations have soliton-like solutions and the electron beam after saturation of the instability relaxes to its initial, weakly perturbed state, provided that only one harmonic of the plasma and the beam density is taken into account. The analytical solutions obtained here for this case correlate well with the numerical ones. A more general model that accounts for the generation of higher harmonics of the plasma and the beam density does not yield soliton-like solutions for the time evolution of the amplitudes of the plasma and beam waves. In such a model, the instability will be collective again: it can be described analytically (at least, up to the time at which it saturates) by using equations with cubic nonlinearities and the method of expansion of the electron trajectories and momenta.     

Saturation of two-stream instability of an electron beam in plasma

The development and nonlinear saturation of two-stream instability of a warm nonrelativistic electron beam in a cold plasma are investigated numerically in the framework of a one-dimensional model. It is shown that, for a sufficiently large velocity spread of the electron beam, instability develops and saturates according to a universal law, the wave phase velocity remains the same in the saturation stage, and the maximum field is somewhat lower than that predicted by classical estimates and depends in a different way on the growth rate. The damping of plasma oscillations not only changes the instability growth rate, but also substantially decreases the maximum wave field.     

Ionization instability and dusty plasma structurization

In the presence of ionization processes, a homogeneous equilibrium dust distribution often appears as a balance between plasma generation by ionization and plasma absorption by dust particles. It is shown that such equilibrium, often present in laboratory plasmas, is generally unstable against the formation of dust clumps separated by dust-free regions (dust voids). The driving force that separates an initially homogeneous dusty plasma into dust clumps and dust voids is the drag force produced by ions flowing out from the regions with reduced dust density. The lower the dust density, the lower the electron absorption by dust particles and the larger the ionization rate proportional to the electron density. An increase in the ion drag force leads to a further decrease in the dust density and, thus, drives the instability. In the nonlinear stage, the instability creates structures—dust clouds separated by dust voids. The dependence of the instability growth rate on the wavenumber (or, in other words, on the size of the dust-free and dust-containing regions) is investigated. It is shown that, for sufficiently small wavenumbers, a homogeneous distribution is always unstable. An analogy with a gravitational-like instability related to shadowing of the plasma flux by dust particles is pointed out. This effect, which is due to collective shadowing of the plasma flux, dominates the shadowing by individual dust particles discussed previously. Similar to the usual gravitational instability, perturbations with the largest scales are always unstable. Contrary to the usual gravitational instability, the largest growth rate corresponds not to the largest possible scale but to the size close to the mean free path of plasma particles colliding with dust particles. A special investigation is undertaken to determine the influence of the ion-neutral collisions on the growth rate of the instability.     

Adaptation of interacting populations to the environmental temperature regime

The biological process of the passing of individuals from the active to the passive state when unfavourable environmental conditions occur has been formalized. This leads to a universal linear superstructing to nonlinear models of ecosystems. At certain rates of this jump, a stabilization of the oscillation instability is possible, and an increase in population vitality can occur. The adaptation processes were examined, and the areas of evolutionarily stable parameters for interacting population (competitors and antagonists) on regular temperature changes were found. A possibility of cyclic changes of parameters in the "prey-predator" system was shown.     

Theory of the anomalous resistivity of a randomly inhomogeneous plasma

The effect of random density inhomogeneities on the anomalous plasma resistivity caused by a current-driven ion acoustic instability is considered. It is shown that, under certain conditions, dissipation due to the plasma inhomogeneity can be more efficient than that due to nonlinear effects. The scenario under consideration can occur in the low-density corona of a high-density Z-pinch.     

Nonlinear dispersion in a plasma with a relativistic electron beam

The nonlinear interaction of a relativistic electron beam with a plasma is investigated numerically on the basis of the extended notions of the physical quantities that enter the linear dispersion relation. Extending the notions of the wave frequency, wavenumber, and wave phase velocity to the nonlinear stage of an instability makes it possible to analyze the evolution of the Cherenkov and plasma resonances and to study how they affect the saturation of the wave amplitude. A model of the beam-plasma instability in which the growth rate is calculated from the corresponding linear hydrodynamic formula on the basis of the results obtained using a numerical kinetic model makes it possible to establish the applicability range of the hydrodynamic approximation for beams with different energies.     

Plasma Crystal as a Time Crystal

Plasma Physics Reports - The nonlinear development stage is studied of the instability of coupled waves in the planar plasma crystal in the external confining force field. It is assumed that the...